Expected Value - Expectation of Matrices

Expectation of Matrices

If X is an m × n matrix, then the expected value of the matrix is defined as the matrix of expected values:

\operatorname{E} = \operatorname{E} \left [\begin{pmatrix} x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\ x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ x_{m,1} & x_{m,2} & \cdots & x_{m,n} \end{pmatrix} \right ] = \begin{pmatrix} \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \vdots & \vdots & \ddots & \vdots \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \end{pmatrix}.

This is utilized in covariance matrices.

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